|
%I #14 Aug 02 2021 07:48:37
%S 102247563,7972318200,477859512889,26234041133443,1405508547112670,
%T 75638497021149062,4150321205365373610,234104217274598884642,
%U 13636766011245325587353,822369813313954835099742,51404873131596488549863350,3332014222322664690079709532
%N Number of transitive reflexive early confluent binary relations R on n labeled elements with max_{x}(|{y : xRy}|) = 10.
%C R is early confluent iff (xRy and xRz) implies (yRz or zRy) for all x, y, z.
%D A. P. Heinz (1990). Analyse der Grenzen und Möglichkeiten schneller Tableauoptimierung. PhD Thesis, Albert-Ludwigs-Universität Freiburg, Freiburg i. Br., Germany.
%H Alois P. Heinz, <a href="/A218091/b218091.txt">Table of n, a(n) for n = 10..200</a>
%F E.g.f.: t_10(x)-t_9(x), with t_k(x) = exp (Sum_{m=1..k} x^m/m! * t_{k-m}(x)) if k>=0 and t_k(x) = 0 else.
%F a(n) = A210918(n) - A210917(n).
%p t:= proc(k) option remember; `if`(k<0, 0,
%p unapply(exp(add(x^m/m! *t(k-m)(x), m=1..k)), x))
%p end:
%p egf:= t(10)(x)-t(9)(x):
%p a:= n-> n!* coeff(series(egf, x, n+1), x, n):
%p seq(a(n), n=10..22);
%t m = 10; t[k_] := t[k] = If[k<0, 0, Function[x, Exp[Sum[x^m/m!*t[k-m][x], {m, 1, k}]]]] ; egf = t[m][x]-t[m-1][x]; a[n_] := n!*Coefficient[Series[egf, {x, 0, n+1}], x, n]; Table[a[n], {n, m, 22}] (* _Jean-François Alcover_, Feb 14 2014, after Maple *)
%Y Column k=10 of A135313.
%K nonn
%O 10,1
%A _Alois P. Heinz_, Oct 20 2012
|
